IndisputableMonolith.QFT.RS_QFT_Structural_001
Structural certificate module for Recognition Science QFT: it packages a domain cost functional, its nonnegativity and evaluation identities, and a strictly positive canonical threshold into an inhabited certificate record. QFT bridge authors cite it when they need a single inhabited witness that the cost/threshold skeleton is in place before continuum or propagator arguments. The module is mostly definitions plus elementary positivity and equality lemmas.
claimThe module introduces a domain cost $C$ on the RS QFT side, proves $C \ge 0$ and the pointwise evaluation identity for $C$, fixes a canonical threshold $\theta > 0$, and packages these facts into an inhabited structural certificate $\mathrm{RSQFTStructural001Cert}$.
background
Recognition Science builds continuum QFT structure on the discrete recognition cost $J$ and the native time quantum $\tau_0 = 1$ tick from the Constants layer. The Cost import supplies the $J$-cost calculus (the unique cost forced by the Recognition Composition Law and T5 uniqueness).
This module sits at the QFT boundary: it does not yet construct propagators or spectra. It only freezes the minimal structural data a later continuum argument needs: a domain-level cost functional, its elementary analytic properties, and a positive numerical threshold against which defects or cutoffs can be compared.
Sibling definitions name that cost (domainCost), the evaluation and nonnegativity facts, the threshold (canonicalThreshold with positivity), and the certificate record that bundles them.
proof idea
Definition-heavy module with short supporting lemmas. The cost and threshold are introduced by definition; nonnegativity and the evaluation identity are proved by direct unfolding against the Cost layer; positivity of the threshold is a one-line arithmetic fact. The certificate type is a structure packing those properties, and inhabitation is by assembling the already-proved fields. No deep tactic scripts or external analytic machinery.
why it matters in Recognition Science
Gives the QFT side a single, named structural witness before continuum or scattering work begins. Downstream used-by edges are empty in the current graph, so the module is a leaf certificate rather than an intermediate lemma in a long chain. It anchors the RS-native cost language (from Cost and Constants) inside the QFT domain so later modules can assume nonnegativity and a positive cutoff without re-proving them. Framework landmarks touched only indirectly: the $J$-cost uniqueness (T5) and the native tick $\tau_0$ that set the units in which the threshold lives.
scope and limits
- Does not construct QFT propagators, spectra, or scattering amplitudes.
- Does not prove uniqueness of the domain cost beyond the packaged identities.
- Does not derive the numerical value of the threshold from T0–T8 forcing.
- Does not connect the certificate to continuum limits or renormalization.
- Does not assert any mass-ladder or alpha-band claim.